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Infinitely Continued III (Posted on 2010-02-04)

Evaluate:

√(6+2√(7+3√(8+4√(9+5√(10+ ....)))))

See The Solution Submitted by K Sengupta

Rating: 4.5000 (2 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)

re: Is my reasoning valid?

| Comment 3 of 7 |

(In reply to Is my reasoning valid? by Jer)

Jer:

I don't think your "proof' is quite valid either, but I certainly think you are on to something.

The expression is not infinite for x <=2, and by substitution we can see easily enough that f(2) = 2

But I don't see offhand how to use induction to get f(3) = 3,

because (f(x)^2 - x - 2)/(x-2) is undefined when x = 2

If we could prove that f(3) = 3, then it follows that f(x) = x.

Posted by Steve Herman on 2010-02-04 18:00:52

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